Geogrid is a widely used geosynthetic material in civil engineering, and its interaction characteristics with fill soil play a crucial role in the stability of reinforced soil structures. This paper investigates the influences of factors such as normal stress, geogrid type, fill moisture content, and compaction on the reinforcement effect, and utilizes grey relational analysis to analyze the degree of influence of each factor. The research findings indicate that, under the same conditions, biaxial geogrid reinforced soil exhibits significantly higher apparent friction angle and maximum shear stress compared to uniaxial geogrid reinforced soil. With the increase of normal stress, the maximum shear stress between the soil and geogrid increases, while the apparent friction angle slightly decreases. Furthermore, higher fill compaction leads to a larger apparent friction angle between the soil and geogrid, while higher moisture content leads to a smaller apparent friction angle. Based on the grey relational analysis ranking, the degree of influence of each factor from highest to lowest is geogrid type > compaction > moisture content > normal stress. Therefore, it is recommended to use biaxial geogrid for reinforced soil in engineering projects, improve the compaction of subgrade soil, and appropriately reduce the moisture content to achieve optimal geogrid reinforcement effects. Additionally, an elastic-exponential hardening model is proposed based on the classical bilinear model to describe and analyze the interface behavior of biaxial geogrid reinforced clay, which can provide guidance for clay reinforcement projects.